Theorem addsridd

Description: Surreal addition to zero is identity. Part of Theorem 3 of Conway p. 17. (Contributed by Scott Fenton, 20-Aug-2024)

	Ref	Expression
Hypothesis	addsridd.1	⊢ ( 𝜑 → 𝐴 ∈ No )
Assertion	addsridd	⊢ ( 𝜑 → ( 𝐴 +s 0s ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		addsridd.1	⊢ ( 𝜑 → 𝐴 ∈ No )
2		addsrid	⊢ ( 𝐴 ∈ No → ( 𝐴 +s 0s ) = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 +s 0s ) = 𝐴 )